IncTSVD:多维数据流的增量张量单数值分解
概括
我们介绍了IncTSVD,这是一种在线方法,用于流动张量数据的增量张量奇数值分解 (TSVD). 这种方法有效地处理有限的内存,并减少与现有的张量分解方法相比的计算成本.
科学领域:
- 数字分析 数字分析
- 数据科学数据科学数据科学
- 张量计计算 张量计计算
背景情况:
- 张量单数值分解 (TSVD) 对于分析多维数据至关重要.
- 现有的TSVD方法通常需要大批次计算,限制其使用流数据或有限的内存.
- 对矩阵的增量奇数值分解 (SVD) 为更新分解提供了一个先例.
研究的目的:
- 开发一个在线算法,以在第三阶段张量数序列上逐步计算TSVD.
- 为了解决基于批次的TSVD方法在传输张量数据和内存约束方面的局限性.
- 将增量矩阵SVD的概念扩展到张量分析的领域.
主要方法:
- 在IncTSVD算法逐步计算TSVD使用张量-张量概念.
- 它保持了以前数据的基础张量,并将TSVD近似与传入的张量数据更新.
- 在合成和现实数据集上进行了理论分析和广泛的数值实验.
主要成果:
- 与现有的基于t产品的张量分解相比,IncTSVD表现出更高的计算和存储效率.
- 该方法的准确性与标准TSVD相提并论.
- 数字实验验证了计算成本和近似误差的理论分析.
结论:
- IncTSVD是一种有效的在线增量计算方法,用于流动张量数据的TSVD.
- 该算法在计算和存储成本方面提供了显著的优势,使其适用于内存有限的环境.
- IncTSVD为动态数据流提供了批量张量分解技术的可行替代方案.
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